Magnetohydrodynamics
In physics and engineering, magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is a model of electrically conducting fluids that treats all interpenetrating particle species together as a single continuous medium.
It is primarily concerned with the low-frequency, large-scale, magnetic behavior in plasmas and liquid metals and has applications in multiple fields including space physics, geophysics, astrophysics, and engineering.
As with any fluid description to a kinetic system, a closure approximation must be applied to highest moment of the particle distribution equation.
[7]: 6 A fundamental concept underlying ideal MHD is the frozen-in flux theorem which states that the bulk fluid and embedded magnetic field are constrained to move together such that one can be said to be "tied" or "frozen" to the other.
in the induction equation vanishes giving the ideal induction equation,[7]: 23 Ideal MHD is only strictly applicable when: In an imperfectly conducting fluid the magnetic field can generally move through the fluid following a diffusion law with the resistivity of the plasma serving as a diffusion constant.
This means that solutions to the ideal MHD equations are only applicable for a limited time for a region of a given size before diffusion becomes too important to ignore.
An MHD wave propagating at an arbitrary angle θ with respect to the time independent or bulk field B0 will satisfy the dispersion relation where is the Alfvén speed.
MHD waves and oscillations are a popular tool for the remote diagnostics of laboratory and astrophysical plasmas, for example, the corona of the Sun (Coronal seismology).
When this is not the case, or the interest is in smaller spatial scales, it may be necessary to use a kinetic model which properly accounts for the non-Maxwellian shape of the distribution function.
However, because MHD is relatively simple and captures many of the important properties of plasma dynamics it is often qualitatively accurate and is therefore often the first model tried.
Effects which are essentially kinetic and not captured by fluid models include double layers, Landau damping, a wide range of instabilities, chemical separation in space plasmas and electron runaway.
In the case of ultra-high intensity laser interactions, the incredibly short timescales of energy deposition mean that hydrodynamic codes fail to capture the essential physics.
The liquid outer core moves in the presence of the magnetic field and eddies are set up into the same due to the Coriolis effect.
[19] Based on the MHD equations, Glatzmaier and Paul Roberts have made a supercomputer model of the Earth's interior.
[22] On December 9, 2010, geoscientists announced that the DEMETER satellite observed a dramatic increase in ULF radio waves over Haiti in the month before the magnitude 7.0 Mw 2010 earthquake.
[23] Researchers are attempting to learn more about this correlation to find out whether this method can be used as part of an early warning system for earthquakes.
Areas researched within space physics encompass a large number of topics, ranging from the ionosphere to auroras, Earth's magnetosphere, the Solar wind, and coronal mass ejections.
Intense solar storms have the potential to cause extensive damage to satellites[27] and infrastructure, thus it is crucial that such events are detected early.
That conservation would imply that as the mass concentrated in the center of the cloud to form the Sun, it would spin faster, much like a skater pulling their arms in.
[31][32] MHD describes a wide range of physical phenomena occurring in fusion plasmas in devices such as tokamaks or stellarators.
The Grad-Shafranov equation derived from ideal MHD describes the equilibrium of axisymmetric toroidal plasma in a tokamak.
In tokamak experiments, the equilibrium during each discharge is routinely calculated and reconstructed, which provides information on the shape and position of the plasma controlled by currents in external coils.
Magnetohydrodynamic sensors are used for precision measurements of angular velocities in inertial navigation systems such as in aerospace engineering.
[33] MHD is related to engineering problems such as plasma confinement, liquid-metal cooling of nuclear reactors, and electromagnetic casting (among others).
The first prototype of this kind of propulsion was built and tested in 1965 by Steward Way, a professor of mechanical engineering at the University of California, Santa Barbara.
Way, on leave from his job at Westinghouse Electric, assigned his senior-year undergraduate students to develop a submarine with this new propulsion system.
[35] MHD power generation fueled by potassium-seeded coal combustion gas showed potential for more efficient energy conversion (the absence of solid moving parts allows operation at higher temperatures), but failed due to cost-prohibitive technical difficulties.
In microfluidics, MHD is studied as a fluid pump for producing a continuous, nonpulsating flow in a complex microchannel design.
[40] Two simulation examples are 3D MHD with a free surface for electromagnetic levitation melting,[41] and liquid metal stirring by rotating permanent magnets.
[42] An important task in cancer research is developing more precise methods for delivery of medicine to affected areas.
